CN108733031B - Network control system fault estimation method based on intermediate estimator - Google Patents

Network control system fault estimation method based on intermediate estimator Download PDF

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CN108733031B
CN108733031B CN201810566420.4A CN201810566420A CN108733031B CN 108733031 B CN108733031 B CN 108733031B CN 201810566420 A CN201810566420 A CN 201810566420A CN 108733031 B CN108733031 B CN 108733031B
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CN108733031A (en
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王越男
王申全
姜玉莲
刘克平
纪文呈宇
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Changchun University of Technology
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
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Abstract

The invention discloses a fault estimation method based on an intermediate estimator network control system, and belongs to the field of fault diagnosis and fault-tolerant control. The invention can estimate the fault of the network control system with signal fading and time-varying time lag under the condition of unknown fault and derivative range thereof. First, an intermediate variable is introduced and an intermediate estimator is constructed to estimate simultaneous states and faults. Then, based on the Lyapunov stability theory and a linear matrix inequality method, the gain of the filter is solved, and sufficient conditions for the stability of the dynamic error system index are obtained. And a congruence transformation method is adopted to remove the design constraint conditions to obtain a feasible result with less conservation. Finally, simulation experiment results illustrate the effectiveness of the proposed method. The method can accurately track and estimate the fault without constraint of observer matching conditions, and is more suitable for an actual network control system.

Description

Network control system fault estimation method based on intermediate estimator
Technical Field
The invention belongs to the field of fault diagnosis and fault-tolerant control, and particularly relates to a fault estimation method based on an intermediate estimator network control system.
Background
With the rapid development of scientific technology, dynamic control systems become more and more complex, and if some elements fail, the whole system is broken down, so that the method has a great significance for improving the reliability and safety of the system and equipment. The fault detection and isolation technology (FDI) is continuously developed under this background, and provides strong technical support and reliable guarantee for improving the safe and reliable operation of the system. The network control system adopts a real-time network to form a feedback control system, and is a control system for realizing information exchange among system components (controllers, actuators, sensors and the like) belonging to different areas by utilizing a communication network. However, introducing networks into the control problem also introduces many new problems. For example, since the NCS uses a communication network as a transmission medium, there are inevitable problems of network-induced delay, packet loss, and the like, so that it is difficult to directly apply the conventional control method to the NCS. It is well known that skew can degrade system performance and can even cause system instability. Therefore, the research on the network control system with time lag and signal fading has very important practical significance. The basic idea of fault detection and isolation is to construct a residual signal to indicate the occurrence of a fault and to determine the type and location of the fault. However, since the residual signal cannot directly reflect the fault, the method is an indirect fault diagnosis technology, and it is difficult to obtain exact fault information only by using a fault detection and isolation technology. Compared to fault detection and isolation, fault estimation enables more detailed information about the fault, such as the magnitude, type, and location of the fault, to be obtained for further fault regulation and fault tolerance control. Therefore, compared to fault detection, fault estimation is more realistic, but the design difficulty is undoubtedly increased, which is a more challenging subject.
Currently, the most common fault estimation design methods mainly include a sliding mode observer-based method, a fault estimation filter-based method, an iterative learning observer-based method, a proportional-integral observer-based method, a neural network observer-based method, an adaptive observer-based method, and the like. Although fault estimation has achieved some research results in recent years, each of these commonly used observer design methods has several critical problems, which greatly limit their application scope, such as:
(1) the research results based on the sliding-mode observer method are relatively more, but the research error system is required to meet SPR conditions, the upper bound of faults needs to be known in advance, and the conditions are very harsh, so that the application of the method is greatly limited;
(2) the method based on the fault estimation filter has generality, but the method requires the open loop of the system to be stable, but the system is usually unstable, so that the application range is limited; meanwhile, the method has stricter constraint on the fault, namely the fault is required to meet f (t) epsilon l 20, infinity), this is only applicable to a very limited class of faults and the fixed-value faults cannot be estimated asymptotically;
(3) the iterative learning observer-based method is complex in design steps and poor in universality;
(4) the method based on the proportional-integral observer has wider application range than that of a sliding-mode observer, an error system is not required to meet an SPR condition, but the method only aims at constant-value faults, time-varying faults are not considered, and systematic design is lacked in the performance of fault estimation;
(5) the fault estimation method based on the adaptive observer is simple in design and high in applicability, and can adaptively asymptotically estimate the upper bound of a fixed-value fault, so that the constraint condition for the fault is relaxed relative to other design methods, but the current CAFE algorithm cannot be applied to a fast time-varying fault, and an error system is required to meet a strict SPR condition.
Compared with the fault estimation of a time-lag-free system, the research on the fault estimation of the time-lag system increases the design difficulty to a certain extent and obviously has more challenges. Existing fault estimation methods all need to meet observer matching conditions, however, in an actual control system, the matching conditions are difficult to meet. Therefore, a new method for estimating the failure of the network control system with signal fading and time-varying delay is needed. The method provided by the invention can well carry out fault estimation on the system without constraint of observer matching conditions, and is more suitable for an actual network control system.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the defect that the fault estimation of the system in the prior art needs observer matching condition constraint, the invention provides a network control system fault estimation method based on an intermediate estimator.
The technical scheme adopted by the invention comprises the following steps:
(1) providing a state space expression of a linear network control system with signal fading and time-varying time lag;
(2) through the analysis of the network control system, the process of measuring the lost data packet meets mutually independent white noise sequences, and then an expression of measurement output is given;
(3) introducing an intermediate variable, and designing a fault estimation filter based on an intermediate estimator;
(4) defining an error variable to obtain a dynamic error system, and solving the gain of the fault estimation filter through a linear matrix inequality;
(5) according to the solved fault estimation filter gain, proving a sufficient condition of stable index of the dynamic error system;
(6) simulation experiments show that the designed fault estimation filter gain based on the intermediate estimator can enable a dynamic error system to be finally and consistently bounded, the exponent is stable, and meanwhile, the fault estimation can accurately track the fault;
preferably, step (3) comprises the sub-steps of:
(01) an intermediate estimator is designed, first introducing an intermediate variable ξ (t) having the form:
(t)＝f(t)-Kx(t)
wherein K has the form:
K＝ωET
(02) then, the intermediate variables are differentiated to obtain:
Figure GDA0002735278030000021
the intermediate variable-based intermediate estimation filter that the clean-up can result in a design has the form:
Figure GDA0002735278030000022
Figure GDA0002735278030000023
Figure GDA0002735278030000031
Figure GDA0002735278030000032
Figure GDA0002735278030000033
in the above formula
Figure GDA0002735278030000034
And
Figure GDA0002735278030000035
is x (t), ξ (t),
Figure GDA0002735278030000036
and f (t), ω being a scalar quantity.
The step (4) comprises the following substeps:
(01) establishing a dynamic error system, firstly defining the following error variables:
Figure GDA0002735278030000037
Figure GDA0002735278030000038
Figure GDA0002735278030000039
Figure GDA00027352780300000310
(02) the error variable is then derived to obtain the error system as follows:
Figure GDA00027352780300000311
Figure GDA00027352780300000312
(03) the filter gain is solved by the following linear matrix inequality:
Figure GDA00027352780300000313
wherein
＝φ1+φ2+φ3+φ4
Figure GDA00027352780300000319
Figure GDA00027352780300000314
Figure GDA00027352780300000315
Figure GDA00027352780300000316
Z＝[e1-e3,e1+e3-2e5,e3-e4,e3+e4-2e6]
Figure GDA00027352780300000317
Figure GDA00027352780300000318
em＝[0n×(m-1)n,In×n,0n×(6-m)n]T,m＝1,2,3,...,6
Figure GDA0002735278030000041
P, Q in the above formula1、Q2、Q3And R are both positive definite symmetric real matrices, G is an arbitrary matrix, is a scalar greater than zero, λ, and ω are both given scalars, and P, G, L are solved by the above formula by L ═ G (GP)-1)TAnd (4) obtaining.
The step (5) comprises the following substeps:
(01) first, define the Lyapunov function:
V(t)＝V1(t)+V2(t)+e-λtV3(t)+e-λtV4(t)
wherein
V1(t)＝ex T(t)Pex(t)
V2(t)＝eξ T(t)-1eξ(t)
Figure GDA0002735278030000042
Figure GDA0002735278030000043
In the above formula-1＝I。
(02) The Lyapunov function is derived to obtain the following form:
Figure GDA0002735278030000044
Figure GDA0002735278030000045
Figure GDA0002735278030000046
Figure GDA0002735278030000047
wherein
Figure GDA0002735278030000048
(03) Combining a Jenson inequality method, a reciprocal convex combination method and a Wirtinger integral inequality method to arrange to obtain the following inequalities:
Figure GDA0002735278030000049
wherein
Figure GDA0002735278030000051
Figure GDA0002735278030000052
Figure GDA0002735278030000053
(04) Knowing xi < 0, the following inequality holds with the congruence transformation method:
Figure GDA0002735278030000054
collation can yield the following inequality:
Figure GDA0002735278030000055
left multiplication of the above
Figure GDA0002735278030000056
Right multiplication by
Figure GDA0002735278030000057
The following inequality holds:
Figure GDA0002735278030000058
by using the schur complement theorem, the following inequality holds:
Figure GDA0002735278030000059
the inequality relationship can be obtained as follows:
Figure GDA00027352780300000510
(05) definition if (e)x(t),eξ(t) e Δ, Δ set having the form:
Figure GDA00027352780300000511
then canCan obtain
Figure GDA00027352780300000512
Thereby being capable of being pushed out
Figure GDA00027352780300000513
The inequality relation can obtain that the dynamic error system is finally consistent and bounded, and the judgment error dynamic system is stable exponentially and is higher than e-λtConverges to the complement of the set delta.
The invention has the beneficial effects that: compared with the prior art, the main contributions of the proposed method are as follows:
(1) in the present invention, the limits of the fault and its derivative may be unknown.
(2) If the fault is constant, the designed intermediate estimator can ensure that the error system state converges exponentially to zero.
(3) Under the condition of not being constrained by observer matching conditions, a new fault estimation method is provided, namely an intermediate estimator is designed for a network control system with signal fading and time-varying time lag. Unlike most existing methods, the design of the intermediate estimator does not rely on the constraints of the equation solution, and is less conservative. By fully utilizing the fault distribution matrix, introducing an intermediate variable and constructing an intermediate estimator, the state and the fault can be estimated simultaneously.
Drawings
FIG. 1 is a block diagram of a closed-loop fault estimation of a linear time-lag network control system;
FIG. 2 shows the fault f (t) and the estimated value of the fault
Figure GDA0002735278030000061
FIG. 3 is the error of the fault estimation ef(t)；
FIG. 4 is a diagram of state estimation error ex(t)；
FIG. 5 is a system state x1(t) and estimation thereofEvaluating value
Figure GDA0002735278030000062
FIG. 6 is system state x2(t) and its estimated value
Figure GDA0002735278030000063
Detailed Description
The method for estimating the fault of the network control system based on the intermediate estimator comprises the following steps:
step one, providing a state space expression of a linear network control system with signal fading and time-varying time lag:
Figure GDA0002735278030000064
Figure GDA0002735278030000065
in the above formula, x (t) epsilon RnIs the state vector, u (t) e RmRepresenting a control input, f (t) ε RlIndicating the fault to be estimated and,
Figure GDA0002735278030000066
is given as an initial condition, AhAnd B, E are constant matrices of appropriate dimensions. A positive integer h (t) represents a time-varying time lag and satisfies 0 ≦ h (t ≦ h,
Figure GDA0002735278030000067
step two, the data packet loss phenomenon often occurs in the network system, and the process of measuring the lost data packet can be described as follows:
y(t)＝α(t)Cx(t)
wherein y (t) e RpIs the measurement of the output vector of the device,c is a known real constant matrix with the appropriate dimensions, and the random variable α (t) is a white noise sequence satisfying the bernoulli distribution and satisfies the following relationship:
Figure GDA0002735278030000068
Figure GDA0002735278030000069
step three, designing an intermediate estimator, and firstly introducing an intermediate variable xi (t) which has the following form:
(t)＝f(t)-Kx(t)
then, the intermediate variables are differentiated to obtain:
Figure GDA00027352780300000610
the intermediate variable-based intermediate estimation filter that the clean-up can result in a design has the form:
Figure GDA00027352780300000611
Figure GDA00027352780300000612
Figure GDA0002735278030000071
Figure GDA0002735278030000072
Figure GDA0002735278030000073
in the above formula
Figure GDA0002735278030000074
And
Figure GDA0002735278030000075
is x (t), ξ (t),
Figure GDA0002735278030000076
and f (t) an estimated value. K has the following form:
K＝ωET
in the above equation, ω is a scalar.
Step four, establishing an error system, firstly defining the following error variables:
Figure GDA0002735278030000077
Figure GDA0002735278030000078
Figure GDA0002735278030000079
Figure GDA00027352780300000710
the error variable is then derived to obtain the error system as follows:
Figure GDA00027352780300000711
Figure GDA00027352780300000712
step five, solving the gain of the filter through the following linear matrix inequality:
Figure GDA00027352780300000713
wherein
＝φ1+φ2+φ3+φ4
Figure GDA00027352780300000714
Figure GDA00027352780300000715
Figure GDA00027352780300000716
Figure GDA00027352780300000717
Z＝[e1-e3,e1+e3-2e5,e3-e4,e3+e4-2e6]
Figure GDA00027352780300000718
Figure GDA00027352780300000719
em＝[0n×(m-1)n,In×n,0n×(6-m)n]T,m＝1,2,3,...,6
Figure GDA0002735278030000081
P, Q in the above formula1、Q2、Q3And R are both positive definite symmetric real matrices, G is an arbitrary matrix, is a scalar greater than zero, and λ, and ω are both given scalars. By the above formula, P, G, L is obtained by L ═ GP-1)TAnd (4) obtaining.
Meanwhile, the method of the embodiment also proves the sufficient condition for the index stability of the dynamic error system, and the method for proving the index stability of the dynamic error system comprises the following steps:
defining a Lyapunov function:
V(t)＝V1(t)+V2(t)+e-λtV3(t)+e-λtV4(t)
wherein
V1(t)＝ex T(t)Pex(t)
V2(t)＝eξ T(t)-1eξ(t)
Figure GDA0002735278030000082
Figure GDA0002735278030000083
In the above formula-1I. The Lyapunov function is derived to obtain the following form:
Figure GDA0002735278030000084
Figure GDA0002735278030000085
Figure GDA0002735278030000086
Figure GDA0002735278030000087
wherein
Figure GDA0002735278030000088
Combining a Jenson inequality method, a reciprocal convex combination method and a Wirtinger integral inequality method to arrange to obtain the following inequalities:
Figure GDA0002735278030000089
wherein
Figure GDA0002735278030000091
Figure GDA0002735278030000092
Figure GDA0002735278030000093
Knowing xi < 0, the following inequality holds with the congruence transformation method:
Figure GDA0002735278030000094
collation can yield the following inequality:
Figure GDA0002735278030000095
left multiplication of the above
Figure GDA0002735278030000096
Right multiplication by
Figure GDA0002735278030000097
The following inequality holds:
Figure GDA0002735278030000098
by using the schur complement theorem, the following inequality holds:
Figure GDA0002735278030000099
the inequality relationship can be obtained as follows:
Figure GDA00027352780300000910
II, define if (e)x(t),eξ(t) e Δ, Δ set having the form:
Figure GDA00027352780300000911
can then obtain
Figure GDA00027352780300000912
Thereby being capable of being pushed out
Figure GDA00027352780300000913
The inequality relation can obtain that the dynamic error system is finally consistent and bounded, and the judgment error dynamic system is stable exponentially and is higher than e-λtConverges to the set delta complement.
In the method for estimating the fault of the network control system based on the intermediate estimator, the Matlab2014b software is used to perform simulation verification on the invented fault estimation method:
(1) selecting the following network control system parameters:
Figure GDA0002735278030000101
C1＝[-1.20.3]，
Figure GDA0002735278030000102
assuming that the time-varying lag h (t) satisfies h (t) 0.585+0.585sin (0.086t), and is selected to be 1, λ 0.5, ω 0.8,
Figure GDA0002735278030000103
controller gain K ═ ω ET＝[-0.8,0.08]The gain of the fault estimation filter can be obtained through a Matlab linear matrix inequality tool box
Figure GDA0002735278030000104
And designed 0.7170.
To better reveal the relationship between the upper time lag bound h and the exponential stability factor λ, table 1 is given. It can be seen from table 1 that the larger the time lag upper bound h is, the smaller the exponential stability coefficient λ is, and the slower the curve convergence speed is.
TABLE 1 maximum time lag upper bound h under different exponential stability coefficients λ
Figure GDA0002735278030000105
To better demonstrate the effectiveness of the proposed method, the following fault signals were chosen:
Figure GDA0002735278030000106
the results show that: we can get the fault f (t) and its estimated value
Figure GDA0002735278030000107
The simulation image of (2) is shown in FIG. 2, and the fault error simulation image is shown in FIG. 3The state estimation error simulation curve is shown as the state vector x shown in FIG. 41(t)，x2(t) and its estimated value
Figure GDA0002735278030000108
Figure GDA0002735278030000109
The simulation curves of (2) are shown in fig. 5 and 6. It can be seen from the simulation curve that the designed fault estimation filter can accurately track and estimate the fault, and the dynamic error system is also finally consistent and bounded and exponentially stable.

Claims (1)

1. A network control system fault estimation method based on an intermediate estimator comprises the following steps:
step one, providing a state space expression of a linear network control system with signal fading and time-varying time lag:
Figure FDA0002735278020000011
Figure FDA0002735278020000012
wherein x (t) e RnIs the state vector, u (t) e RmRepresenting a control input, f (t) ε RlIndicating the fault to be estimated and,
Figure FDA0002735278020000013
is given as an initial condition, AhB and E are constant matrixes, positive integers h (t) represent time-varying time lag and satisfy the following relation:
0≤h(t)≤h
Figure FDA0002735278020000014
step two, through the analysis of the network control system, the data packet loss phenomenon often occurs in the network system, the process of measuring the lost data packet meets the mutually independent white noise sequence, and then an expression of measurement output is given, and the process of measuring the lost data packet can be described as follows:
y(t)＝α(t)Cx(t)
wherein y (t) e RpIs a measured output vector, C is a known real constant matrix with the appropriate dimensions, and the random variable α (t) is a white noise sequence satisfying a bernoulli distribution and satisfies the following relationship:
Figure FDA0002735278020000015
Figure FDA0002735278020000016
step three, designing an intermediate estimator, and firstly introducing an intermediate variable xi (t) which has the following form:
ξ(t)＝f(t)-Kx(t)
the intermediate variable ξ (t) is then derived to yield:
Figure FDA0002735278020000017
the sorting can result in the designed intermediate variable-based intermediate estimation filter having the form:
Figure FDA0002735278020000018
Figure FDA0002735278020000019
Figure FDA00027352780200000110
Figure FDA0002735278020000021
Figure FDA0002735278020000022
in the above formula
Figure FDA0002735278020000023
And
Figure FDA0002735278020000024
respectively, x (t), ξ (t),
Figure FDA0002735278020000025
and f (t), wherein K has the form:
K＝ωET
in the above formula, ω is a scalar;
step four, establishing a dynamic error system, and firstly defining the following error variables:
Figure FDA0002735278020000026
Figure FDA0002735278020000027
Figure FDA0002735278020000028
Figure FDA0002735278020000029
then for the error variable ex(t) and eξ(t) derivation, resulting in an error system as follows:
Figure FDA00027352780200000210
Figure FDA00027352780200000211
the filter gain L can be solved by the following linear matrix inequality:
Figure FDA00027352780200000212
wherein
φ＝φ1+φ2+φ3+φ4
Figure FDA00027352780200000213
Figure FDA00027352780200000214
Figure FDA00027352780200000215
Figure FDA00027352780200000216
Z＝[e1-e3,e1+e3-2e5,e3-e4,e3+e4-2e6]
Figure FDA0002735278020000031
Figure FDA0002735278020000032
em＝[0n×(m-1)n,In×n,0n×(6-m)n]T,m＝1,2,3,4,5,6
Figure FDA0002735278020000038
P, Q in the above formula1、Q2、Q3R is a positive definite symmetrical real matrix, G is an arbitrary matrix and is a scalar larger than zero, lambda is a given scalar, P and G are solved by the formula, and a filter gain matrix L belongs to Rn×pCan be represented by L ═ GP-1)TObtaining;
step five, according to the solved fault estimation filter gain, proving a sufficient condition for the index stability of the dynamic error system, firstly defining a Lyapunov function:
V(t)＝V1(t)+V2(t)+e-λtV3(t)+e-λtV4(t)
wherein
V1(t)＝exT(t)Pex(t)
V2(t)＝eξ T(t)-1eξ(t)
Figure FDA0002735278020000033
Figure FDA0002735278020000034
In the above formula-1Derivation of the Lyapunov function described above yields the following form:
Figure FDA0002735278020000035
Figure FDA0002735278020000036
Figure FDA0002735278020000037
Figure FDA0002735278020000041
wherein
Figure FDA0002735278020000042
Combining a Jenson inequality method, a reciprocal convex combination method and a Wirtinger integral inequality method to arrange to obtain the following inequalities:
Figure FDA0002735278020000043
wherein
Figure FDA0002735278020000044
Figure FDA0002735278020000045
Figure FDA0002735278020000046
Knowing xi < 0, the following inequality holds with the congruence transformation method:
Figure FDA0002735278020000047
collation can yield the following inequality:
Figure FDA0002735278020000048
left multiplication of the above
Figure FDA0002735278020000049
Right multiplication by
Figure FDA00027352780200000410
The following inequality holds:
Figure FDA00027352780200000411
by using the schur complement theorem, the following inequality holds:
Figure FDA00027352780200000412
the inequality relationship can be obtained as follows:
Figure FDA00027352780200000414
the set of Δ is defined to have the form:
Figure FDA00027352780200000413
if (e)x(t),eξ(t)). epsilon.DELTA.can be obtained
Figure FDA0002735278020000051
Thereby being capable of being pushed out
Figure FDA0002735278020000052
The inequality relationships described above result in a dynamic error system that is ultimately consistently bounded above e-λtThe rate of the error is converged to a set delta complement, and the index of an error dynamic system is ensured to be stable;
and step six, simulation experiments show that the designed fault estimation filter gain based on the intermediate estimator can enable a dynamic error system to be finally and consistently bounded, the exponent is stable, and meanwhile, the fault estimation can accurately track the fault.
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